Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in d=3 and d=6

Details Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in d=3 and d=6 Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in d=3 and d=6

1999-11-17

arxiv.org/abs/hep-th/9911135v3

Nucl.Phys.B578:139-152,2000

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, latex, references added

Scientific paper

10.1016/S0550-3213(99)00822-6

We consider free superconformal theories of n=8 scalar multiplet in d=3 and (2,0) tensor multiplet in d=6 and compute 2-point and 3-point correlators of their stress tensors. The results for the 2-point and 3-point correlators for a single d=3 and d=6 multiplet differ from the "strong-coupling" AdS_4 and AdS_7 supergravity predictions by the factors $4\sqrt2 \over 3\pi}N^{3/2}$ and $4N^3$ respectively. These are the same factors as found earlier in hep-th/9703040 in the comparison of the brane free field theory and the 11-d supergravity predictions for the absorption cross-sections of longitudinally polarized gravitons by multiple M2 and M5 branes. While the correspondence of the results for the cross-sections and 2-point functions was expected on the basis of unitarity, the fact that the same coefficients appear in the ratio of the free-theory and supergravity 3-point functions is non-trivial. Thus, like in the d=4 SYM case, in both d=3 and d=6 theories the ratio of the 3-point and 2-point correlators / is exactly the same in the free field theory and in the interacting CFT as described (to leading order in large $N$) by the 11-d supergravity on AdS_{d+1} x S^{10-d}.